Answer:
the length of the diagonal AC is;
[tex]8[/tex]Explanation:
Given the parallelogram ABCD, diagonals AC and BD intersect at point E.
[tex]\begin{gathered} AE=2x \\ CE=x+2 \\ BE=y+10 \\ DE=4y+8 \end{gathered}[/tex]Recall that the diagonals of a parallelogram bisect each other;
So;
[tex]AE=CE[/tex]substituting AE and CE;
[tex]\begin{gathered} 2x=x+2 \\ 2x-x=2 \\ x=2 \end{gathered}[/tex]To calculate the length of AC;
[tex]\begin{gathered} AC=2x+x+2=3x+2 \\ since\text{ x=2} \\ AC=3x+2=3(2)+2 \\ AC=6+2 \\ AC=8 \end{gathered}[/tex]Therefore, the length of the diagonal AC is;
[tex]8[/tex]